In this video, the teacher explains how to determine if a whole number is a multiple of 4 or 7 using divisibility rules. The teacher demonstrates the rule for divisibility by 4, which involves looking at the last two digits of the number. They also explain the rule for divisibility by 7, which requires circling the digit in the ones place, doubling it, subtracting it from the remaining digits, and checking if the result is divisible by 7.